Last night we solved the Remote Admin / JBoss conflict we had been experiencing.
The root of the problem was found to be the method used to start JBoss as a service. Prior to last night, we had used a 3rd party product called ServiceMill. Last night we switched to use the Run As Service tool that is provided by JBoss. That made the difference. Remote Admin is now able to be used on the server platform without interfering with JBoss.